Scattering of plane elastic waves by a rigid circular cylindrical inclusion imbedded in a random medium

The problem of scattering of a plane elastic wave by a rigid circular cylindrical-inclusion imbedded in a random medium is analyzed on the assumptions that the medium differs slightly from a homogeneous medium, is independent of axial space variable and is statistically homogeneous and isotropic in other space variables. By perturbation method, equations satisfied by the mean wave potentials in the exterior of a thin boundary layer wrapping around the inclusion are derived which are correct through terms of order ϵ², where ϵ measures the randomness of medium. These equations are the same equations satisfied by the wave potentials when ϵ = 0, except the original propagation constants being replaced by their corresponding effective propagation constants. This enables one to treat random problems as deterministic ones of which solutions are usually known. Once the mean wave potentials are found, the mean displacement vector can be calculated in the usual manner.